02_modelFitting_globalTreeModel

Based on code from Martin Holdrege’s Sagebrush-Fire paper

This workflow fits a model across all of CONUS that predicts whether a location does or does not have trees.

The data consists of vegetation % cover by functional group from across CONUS (from AIM, FIA, LANDFIRE, and RAP), as well as climate variables from DayMet, which have been aggregated into mean interannual conditions accross multiple temporal windows.

Dependencies

Set user defined parameters

print(params)

## $run
## [1] FALSE
## 
## $save_figs
## [1] TRUE
## 
## $ecoregion
## [1] "shrubGrass"
## 
## $response
## [1] "TotalTreeCover"
## 
## $removeTexasLouisianaPlain
## [1] FALSE
## 
## $removeAllAnoms
## [1] TRUE
## 
## $trimAnomalies
## [1] FALSE
## 
## $autoKfold
## [1] FALSE
## 
## $whichSecondBestMod
## [1] "auto"

# set to true if want to run for a limited number of rows (i.e. for code testing)
test_run <- params$test_run
save_figs <- params$save_figs
response <- params$response
fit_sample <- TRUE # fit model to a sample of the data
n_train <- 5e4 # sample size of the training data
n_test <- 1e6 # sample size of the testing data (if this is too big the decile dotplot code throws memory errors)
trimAnom <- params$trimAnomalies
removeTLP <- params$removeTexasLouisianaPlain
run <- params$run
autoKfold <- params$autoKfold
removeAllAnoms <- params$removeAllAnoms
whichSecondBestMod <- params$whichSecondBestMod

Load packages and source functions

# set option so resampled dataset created here reproduces earlier runs of this code with dplyr 1.0.10
source("../../../Functions/glmTransformsIterates.R")
source("../../../Functions/transformPreds.R")
source("../../../Functions/betaLASSO.R")

#source("../../../Functions/StepBeta_mine.R")
#source("src/fig_params.R")
#source("src/modeling_functions.R")
 
library(betareg)
library(ggspatial)
library(terra)
library(tidyterra)
library(sf)
library(caret)
library(tidyverse)
library(GGally) # for ggpairs()
library(pdp) # for partial dependence plots
library(gridExtra)
library(knitr)
library(patchwork) # for figure insets etc. 
library(ggtext)
library(StepBeta)
theme_set(theme_classic())
library(here)
library(rsample)
library(kableExtra)
library(glmnet)
library(USA.state.boundaries)

Read in data

Data compiled in the prepDataForModels.R script

here::i_am("Analysis/VegComposition/ModelFitting/02_ModelFitting_globalTreeModel.Rmd")
modDat <- readRDS( here("Data_processed", "CoverData", "DataForModels_spatiallyAveraged_withSoils_noSf_sampledLANDFIRE.rds")) %>% st_drop_geometry()

Prep data

We will fit a binomial model that predicts whether or not there are trees at a location. Because the tree cover data we have is continuous between 0 and 100, we convert it to be binomial be forcing any values ≤ 10% to be 0, and any values > 10% to be 1.

modDat <- modDat %>% 
  mutate(TotalTreeCover_binom = replace(TotalTreeCover, TotalTreeCover <=10, 0)) %>% 
  mutate(TotalTreeCover_binom = replace(TotalTreeCover_binom, TotalTreeCover_binom > 10, 1))

set.seed(1234)
# now, rename columns for brevity
modDat_1 <- modDat %>% 
  dplyr::select(-c(prcp_annTotal:annVPD_min)) %>% 
  # mutate(Lon = st_coordinates(.)[,1], 
  #        Lat = st_coordinates(.)[,2])  %>% 
  # st_drop_geometry() %>% 
  # filter(!is.na(newRegion))
  rename("tmin" = tmin_meanAnnAvg_CLIM, 
     "tmax" = tmax_meanAnnAvg_CLIM, #1
     "tmean" = tmean_meanAnnAvg_CLIM, 
     "prcp" = prcp_meanAnnTotal_CLIM, 
     "t_warm" = T_warmestMonth_meanAnnAvg_CLIM,
     "t_cold" = T_coldestMonth_meanAnnAvg_CLIM, 
     "prcp_wet" = precip_wettestMonth_meanAnnAvg_CLIM,
     "prcp_dry" = precip_driestMonth_meanAnnAvg_CLIM, 
     "prcp_seasonality" = precip_Seasonality_meanAnnAvg_CLIM, #2
     "prcpTempCorr" = PrecipTempCorr_meanAnnAvg_CLIM,  #3
     "abvFreezingMonth" = aboveFreezing_month_meanAnnAvg_CLIM, 
     "isothermality" = isothermality_meanAnnAvg_CLIM, #4
     "annWatDef" = annWaterDeficit_meanAnnAvg_CLIM, 
     "annWetDegDays" = annWetDegDays_meanAnnAvg_CLIM,
     "VPD_mean" = annVPD_mean_meanAnnAvg_CLIM, 
     "VPD_max" = annVPD_max_meanAnnAvg_CLIM, #5
     "VPD_min" = annVPD_min_meanAnnAvg_CLIM, #6
     "VPD_max_95" = annVPD_max_95percentile_CLIM, 
     "annWatDef_95" = annWaterDeficit_95percentile_CLIM, 
     "annWetDegDays_5" = annWetDegDays_5percentile_CLIM, 
     "frostFreeDays_5" = durationFrostFreeDays_5percentile_CLIM, 
     "frostFreeDays" = durationFrostFreeDays_meanAnnAvg_CLIM, 
     "soilDepth" = soilDepth, #7
     "clay" = surfaceClay_perc, 
     "sand" = avgSandPerc_acrossDepth, #8
     "coarse" = avgCoarsePerc_acrossDepth, #9
     "carbon" = avgOrganicCarbonPerc_0_3cm, #10
     "AWHC" = totalAvailableWaterHoldingCapacity,
     ## anomaly variables
     tmean_anom = tmean_meanAnnAvg_3yrAnom, #15
     tmin_anom = tmin_meanAnnAvg_3yrAnom, #16
     tmax_anom = tmax_meanAnnAvg_3yrAnom, #17
    prcp_anom = prcp_meanAnnTotal_3yrAnom, #18
      t_warm_anom = T_warmestMonth_meanAnnAvg_3yrAnom,  #19
     t_cold_anom = T_coldestMonth_meanAnnAvg_3yrAnom, #20
      prcp_wet_anom = precip_wettestMonth_meanAnnAvg_3yrAnom, #21
      precp_dry_anom = precip_driestMonth_meanAnnAvg_3yrAnom,  #22
    prcp_seasonality_anom = precip_Seasonality_meanAnnAvg_3yrAnom, #23 
     prcpTempCorr_anom = PrecipTempCorr_meanAnnAvg_3yrAnom, #24
      aboveFreezingMonth_anom = aboveFreezing_month_meanAnnAvg_3yrAnom, #25  
    isothermality_anom = isothermality_meanAnnAvg_3yrAnom, #26
       annWatDef_anom = annWaterDeficit_meanAnnAvg_3yrAnom, #27
     annWetDegDays_anom = annWetDegDays_meanAnnAvg_3yrAnom,  #28
      VPD_mean_anom = annVPD_mean_meanAnnAvg_3yrAnom, #29
      VPD_min_anom = annVPD_min_meanAnnAvg_3yrAnom,  #30
      VPD_max_anom = annVPD_max_meanAnnAvg_3yrAnom,  #31
     VPD_max_95_anom = annVPD_max_95percentile_3yrAnom, #32
      annWatDef_95_anom = annWaterDeficit_95percentile_3yrAnom, #33 
      annWetDegDays_5_anom = annWetDegDays_5percentile_3yrAnom ,  #34
    frostFreeDays_5_anom = durationFrostFreeDays_5percentile_3yrAnom, #35 
      frostFreeDays_anom = durationFrostFreeDays_meanAnnAvg_3yrAnom #36
  ) %>% 
  dplyr::select(-c(tmin_meanAnnAvg_3yr:durationFrostFreeDays_meanAnnAvg_3yr))

Visualize the predictor variables

The following are the candidate predictor variables for this ecoregion:

  prednames <- c(
    "tmean"               ,"prcp"               ,"prcp_seasonality", "prcpTempCorr"       ,  "isothermality"     ,     
"annWetDegDays"           ,"sand"               ,"coarse"         , "AWHC"                #, "tmin_anom"          ,    
#"tmax_anom"               ,"t_warm_anom", "prcp_wet_anom"      ,"precp_dry_anom" , "prcp_seasonality_anom", "prcpTempCorr_anom" ,     
#"aboveFreezingMonth_anom" ,"isothermality_anom" ,"annWatDef_anom" , "annWetDegDays_anom"  , "VPD_min_anom"     
  )

Scale the predictor variables for the model-fitting process

allPreds <- modDat_1 %>% 
  dplyr::select(tmin:frostFreeDays,tmean_anom:frostFreeDays_anom, soilDepth:AWHC) %>% 
  names()
modDat_1_s <- modDat_1 %>% 
  mutate(across(all_of(allPreds), base::scale, .names = "{.col}_s")) 
saveRDS(modDat_1_s, file = "./models/scaledModelInputData.rds")

Remove the rows that have no observations for total tree cover

# 
modDat_1_s <- modDat_1_s[!is.na(modDat_1_s[,"TotalTreeCover_binom"]),]

# subset the data to only include these predictors, and remove any remaining NAs 
modDat_1_s <- modDat_1_s %>% 
  dplyr::select(prednames, paste0(prednames, "_s"), TotalTreeCover, TotalTreeCover_binom, newRegion, Year, x, y, NA_L1NAME, NA_L2NAME) %>% 
  drop_na()

names(prednames) <- prednames
df_pred <- modDat_1_s[, prednames]

response <- "TotalTreeCover"

Visualize the response variable

ggplot(modDat_1_s) + 
  geom_histogram(aes(TotalTreeCover/100), fill = "darkgreen", col = "darkgreen", alpha = .5) + 
  xlab("Tree Cover") + 
  ggtitle("Untransformed, observed tree cover")

ggplot(modDat_1_s) + 
  geom_histogram(aes(TotalTreeCover_binom), fill = "purple", alpha = .5, col = "purple") +
  xlab("Tree Cover") + 
  ggtitle("Tree cover, converted to binomial with a 10% 'cutoff'")

create_summary <- function(df) {
  df %>% 
    pivot_longer(cols = everything(),
                 names_to = 'variable') %>% 
    group_by(variable) %>% 
    summarise(across(value, .fns = list(mean = ~mean(.x, na.rm = TRUE), min = ~min(.x, na.rm = TRUE), 
                                        median = ~median(.x, na.rm = TRUE), max = ~max(.x, na.rm = TRUE)))) %>% 
    mutate(across(where(is.numeric), round, 4))
}

modDat_1_s[prednames] %>% 
  create_summary() %>% 
  knitr::kable(caption = 'summaries of possible predictor variables') %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

summaries of possible predictor variables

variable	value_mean	value_min	value_median	value_max
AWHC	14.7058	0.0000	14.1164	35.2011
annWetDegDays	1832.3708	85.2713	1596.8830	7131.5166
coarse	9.6208	0.0000	5.7233	79.9649
isothermality	37.8165	19.4935	37.8377	63.5357
prcp	501.4693	47.6797	400.6340	4360.3490
prcpTempCorr	0.0205	-0.8613	0.1010	0.7098
prcp_seasonality	0.9760	0.3568	0.9389	2.2319
sand	46.7510	0.0000	45.5043	99.8184
tmean	11.1297	-2.0557	10.0003	24.9823

Histograms of raw and scaled predictors

scaleFigDat_1 <- modDat_1_s %>% 
  dplyr::select(c(x, y, Year, prednames)) %>% 
  pivot_longer(cols = all_of(names(prednames)), 
               names_to = "predNames", 
               values_to = "predValues_unScaled")
scaleFigDat_2 <- modDat_1_s %>% 
  dplyr::select(c(x, y, Year, paste0(prednames, "_s"))) %>% 
  pivot_longer(cols = all_of(paste0(prednames,"_s"
                                    )), 
               names_to = "predNames", 
               values_to = "predValues_scaled", 
               names_sep = ) %>% 
  mutate(predNames = str_replace(predNames, pattern = "_s$", replacement = ""))

scaleFigDat_3 <- scaleFigDat_1 %>% 
  left_join(scaleFigDat_2)

ggplot(scaleFigDat_3) + 
  facet_wrap(~predNames, scales = "free") +
  geom_histogram(aes(predValues_unScaled), fill = "lightgrey", col = "darkgrey") + 
  geom_histogram(aes(predValues_scaled), fill = "lightblue", col = "blue") +
  xlab ("predictor variable values") + 
  ggtitle("Comparing the distribution of unscaled (grey) to scaled (blue) predictor variables")

modDat_1_s <- modDat_1_s %>% 
  rename_with(~paste0(.x, "_raw"), 
                any_of(names(prednames))) %>% 
  rename_with(~str_remove(.x, "_s$"), 
              any_of(paste0(names(prednames), "_s")))

Predictor variables compared to binned response variables

set.seed(12011993)
# vector of name of response variables
vars_response <- response
# longformat dataframes for making boxplots
df_sample_plots <-  modDat_1_s  %>% 
  slice_sample(n = 5e4) %>% 
   rename(response = all_of("TotalTreeCover_binom")) %>% 
  mutate(response = case_when(
    response == 0 ~ "0", 
    response > 0  ~ "1", 
  )) %>% 
  dplyr::select(c(response, prednames)) %>% 
  tidyr::pivot_longer(cols = unname(prednames), 
               names_to = "predictor", 
               values_to = "value"
               )  
 

  ggplot(df_sample_plots, aes_string(x= "response", y = 'value')) +
  geom_boxplot() +
  facet_wrap(~predictor , scales = 'free_y') + 
  ylab("Predictor Variable Values") + 
    xlab(response)

Model Fitting

Visualize the spatial blocks and how they differ across environmental space

First, if there are observations in Louisiana, sub-sample them so they’re not so over-represented in the dataset

## make data into spatial format
modDat_1_sf <- modDat_1_s %>% 
  st_as_sf(coords = c("x", "y"), crs = st_crs("EPSG:4326"))


# download map info for visualization
data(state_boundaries_wgs84) 

cropped_states <- suppressMessages(state_boundaries_wgs84 %>%
  dplyr::filter(NAME!="Hawaii") %>%
  dplyr::filter(NAME!="Alaska") %>%
  dplyr::filter(NAME!="Puerto Rico") %>%
  dplyr::filter(NAME!="American Samoa") %>%
  dplyr::filter(NAME!="Guam") %>%
  dplyr::filter(NAME!="Commonwealth of the Northern Mariana Islands") %>%
  dplyr::filter(NAME!="United States Virgin Islands") %>%
  sf::st_sf() %>%
  sf::st_transform(sf::st_crs(modDat_1_sf))) 

# if (ecoregion %in% c("Forest", "eastForest", "forest")){
# modDat_1_s$uniqueID <- 1:nrow(modDat_1_s)
# modDat_1_sf$uniqueID <- 1:nrow(modDat_1_sf)
# 
# # find which observations overlap with Louisiana
# obs_LA_temp <- st_intersects(modDat_1_sf, cropped_states[cropped_states$NAME == "Louisiana",], sparse = FALSE)
# if (sum(obs_LA_temp) > 0) {
#  obs_LA_1 <- modDat_1_sf[which(obs_LA_temp == TRUE, arr.ind = TRUE)[,1],]
# # now, find only those within the oversampled area (near the coast)
# dims <- c(xmin = 730439.1, xmax = 1042195.5, ymax = -1222745.2, ymin = -1390430.9)
# badBox <- st_bbox(dims) %>% 
#   st_as_sfc() %>% 
#   st_set_crs(value = st_crs(modDat_1_sf))
#   
# obs_LA_temp2 <- st_intersects(obs_LA_1, badBox, sparse = FALSE)
# obs_LA_2 <- obs_LA_1[which(obs_LA_temp2 == TRUE, arr.ind = TRUE)[,1],]
# 
# # subsample so there aren't so many 
# # get every 7th observation
# obs_LA_sampled <- obs_LA_2[seq(from = 1, to = nrow(obs_LA_2), by = 10),]
# # remove observations that aren't sampled from the larger dataset
# obsToRemove <- obs_LA_2[!(obs_LA_2$uniqueID %in% obs_LA_sampled$uniqueID),]
# 
# modDat_1_sf <- modDat_1_sf[!(modDat_1_sf$uniqueID %in% obsToRemove$uniqueID),]
# modDat_1_s <- modDat_1_s[!(modDat_1_s$uniqueID %in% obsToRemove$uniqueID),] 
# }
#}

## do a pca of climate across level 2 ecoregions
pca <- prcomp(modDat_1_s[,paste0(prednames)])
library(factoextra)
(fviz_pca_ind(pca, habillage = modDat_1_s$NA_L2NAME, label = "none", addEllipses = TRUE, ellipse.level = .95, ggtheme = theme_minimal(), alpha.ind = .1))

# if (ecoregion == "shrubGrass") {
#   print("We'll combine the 'Mediterranean California' and 'Western Sierra Madre Piedmont' ecoregions (into 'Mediterranean Piedmont'). We'll also combine `Tamaulipas-Texas semiarid plain,' 'Texas-Lousiana Coastal plain,' and 'South Central semiarid prairies' ecoregions (into (`Semiarid plain and prairies`)." )
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "WESTERN SIERRA MADRE PIEDMONT"), "NA_L2NAME"] <- "MEDITERRANEAN PIEDMONT"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("TAMAULIPAS-TEXAS SEMIARID PLAIN", "TEXAS-LOUISIANA COASTAL PLAIN", "SOUTH CENTRAL SEMIARID PRAIRIES"), "NA_L2NAME"] <- "SEMIARID PLAIN AND PRAIRIES"
# 
#     modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND WEST COAST FOREST"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "UPPER GILA MOUNTAINS"), "NA_L2NAME"] <- "MEDITERRANEAN CALIFORNIA AND UPPER GILA MOUNTAINS"
# 
# modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS", "OZARK/OUACHITA-APPALACHIAN FORESTS"), "NA_L2NAME"] <- "OZARK/OUACHITA-APPALACHIAN FORESTS AND MIXED WOOD PLAINS"
# #////
# modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "WESTERN SIERRA MADRE PIEDMONT"), "NA_L2NAME"] <- "MEDITERRANEAN PIEDMONT"
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("TAMAULIPAS-TEXAS SEMIARID PLAIN", "TEXAS-LOUISIANA COASTAL PLAIN", "SOUTH CENTRAL SEMIARID PRAIRIES"), "NA_L2NAME"] <- "SEMIARID PLAIN AND PRAIRIES"
# 
#     modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND WEST COAST FOREST"
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "UPPER GILA MOUNTAINS"), "NA_L2NAME"] <- "MEDITERRANEAN CALIFORNIA AND UPPER GILA MOUNTAINS"
# 
# modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS", "OZARK/OUACHITA-APPALACHIAN FORESTS"), "NA_L2NAME"] <- "OZARK/OUACHITA-APPALACHIAN FORESTS AND MIXED WOOD PLAINS"
#  if (response == "CAMCover") {
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MEDITERRANEAN PIEDMONT", "SEMIARID PLAIN AND PRAIRIES"), "NA_L2NAME"] <- "SEMIARID PLAIN AND PRAIRIES AND PIEDMONT"
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MEDITERRANEAN PIEDMONT", "SEMIARID PLAIN AND PRAIRIES"), "NA_L2NAME"] <- "SEMIARID PLAIN AND PRAIRIES AND PIEDMONT"
#  } else if (response %in% c("C4GramCover_prop", "C3GramCover_prop")) {
#      modDat_1_s[modDat_1_s$NA_L2NAME %in% c("SEMIARID PLAIN AND PRAIRIES", "TEMPERATE PRAIRIES"), "NA_L2NAME"] <- "SEMIARID AND TEMPERATE PRAIRIES"
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("SEMIARID PLAIN AND PRAIRIES", "TEMPERATE PRAIRIES"), "NA_L2NAME"] <- "SEMIARID AND TEMPERATE PRAIRIES"
#  }
# 
# } else if (ecoregion == "CONUS") {
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("EVERGLADES", "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"), "NA_L2NAME"] <- "EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND WEST COAST FOREST"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS", "OZARK/OUACHITA-APPALACHIAN FORESTS"), "NA_L2NAME"] <- "OZARK/OUACHITA-APPALACHIAN FORESTS AND MIXED WOOD PLAINS"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "UPPER GILA MOUNTAINS"), "NA_L2NAME"] <- "MEDITERRANEAN CALIFORNIA AND UPPER GILA MOUNTAINS"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("OZARK/OUACHITA-APPALACHIAN FORESTS AND MIXED WOOD PLAINS", "SOUTHEASTERN USA PLAINS",  "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN AND MIXED WOOD PLAINS"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("SOUTH CENTRAL SEMIARID PRAIRIES", "TEXAS-LOUISIANA COASTAL PLAIN"), "NA_L2NAME"] <- "SOUTH CENTRAL SEMIARID PRAIRIES"
#   #///
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("EVERGLADES", "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"), "NA_L2NAME"] <- "EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND WEST COAST FOREST"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS", "OZARK/OUACHITA-APPALACHIAN FORESTS"), "NA_L2NAME"] <- "OZARK/OUACHITA-APPALACHIAN FORESTS AND MIXED WOOD PLAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MEDITERRANEAN CALIFORNIA", "UPPER GILA MOUNTAINS"), "NA_L2NAME"] <- "MEDITERRANEAN CALIFORNIA AND UPPER GILA MOUNTAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("OZARK/OUACHITA-APPALACHIAN FORESTS AND MIXED WOOD PLAINS", "SOUTHEASTERN USA PLAINS",  "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN AND MIXED WOOD PLAINS"
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("SOUTH CENTRAL SEMIARID PRAIRIES", "TEXAS-LOUISIANA COASTAL PLAIN"), "NA_L2NAME"] <- "SOUTH CENTRAL SEMIARID PRAIRIES"
# 
#   if (response %in% c("C4GramCover_prop")) {
#     modDat_1_s[modDat_1_s$NA_L2NAME %in% c("CENTRAL USA PLAINS", "TEMPERATE PRAIRIES", "SOUTHEASTERN AND MIXED WOOD PLAINS", "ATLANTIC HIGHLANDS", "MIXED WOOD SHIELD"), "NA_L2NAME"] <- "EASTERN AND MIXED WOOD PLAINS AND FOREST"
#   #///
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in%c("CENTRAL USA PLAINS", "TEMPERATE PRAIRIES", "SOUTHEASTERN AND MIXED WOOD PLAINS", "ATLANTIC HIGHLANDS", "MIXED WOOD SHIELD"), "NA_L2NAME"] <- "EASTERN AND MIXED WOOD PLAINS AND FOREST"
#   }
# } else if (ecoregion == "forest"  & response != "CAMCover") {
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "EVERGLADES"), "NA_L2NAME"] <- "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS  AND EVERGLADES"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("UPPER GILA MOUNTAINS", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS\tAND EVERGLADES", "SOUTHEASTERN USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN USA PLAINS"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("ATLANTIC HIGHLANDS", "OZARK/OUACHITA-APPALACHIAN FORESTS"), "NA_L2NAME"] <- "HIGHLANDS AND APPALACHIAN FORESTS"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("CENTRAL USA PLAINS", "MIXED WOOD PLAINS"), "NA_L2NAME"] <- "CENTRAL AND MIXED WOOD PLAINS"
# 
#    modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD SHIELD", "CENTRAL AND MIXED WOOD PLAINS"), "NA_L2NAME"] <- "CENTRAL AND MIXED WOOD PLAINS AND MIXED WOOD SHIELD"
# 
#        ## divide southeastern US plains into two regions, since it's by far the largest group
#   modDat_1_s[modDat_1_s$NA_L2NAME == "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS" &
#                modDat_1_s$Long < -966595#-1773969
#                , "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 1"
#   modDat_1_s[modDat_1_s$NA_L2NAME == "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS", "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 2"
#    #///
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "EVERGLADES"), "NA_L2NAME"] <- "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS    AND EVERGLADES"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("UPPER GILA MOUNTAINS", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS\tAND EVERGLADES", "SOUTHEASTERN USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN USA PLAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("ATLANTIC HIGHLANDS", "OZARK/OUACHITA-APPALACHIAN FORESTS"), "NA_L2NAME"] <- "HIGHLANDS AND APPALACHIAN FORESTS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("CENTRAL USA PLAINS", "MIXED WOOD PLAINS"), "NA_L2NAME"] <- "CENTRAL AND MIXED WOOD PLAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD SHIELD", "CENTRAL AND MIXED WOOD PLAINS"), "NA_L2NAME"] <- "CENTRAL AND MIXED WOOD PLAINS AND MIXED WOOD SHIELD"
#           ## divide southeastern US plains into two regions, since it's by far the largest group
#   modDat_1_sf[modDat_1_sf$NA_L2NAME == "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS" &
#               st_coordinates(modDat_1_sf)[,1] < -966595#-1773969
#                 , ]$NA_L2NAME <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 1"
#   modDat_1_sf[modDat_1_sf$NA_L2NAME == "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS", "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 2"
# 
#   if (response %in% c("C3GramCover_prop", "C4GramCover_prop") ) {
#      modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 1"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 1"
#      modDat_1_s[modDat_1_s$NA_L2NAME %in% c("CENTRAL AND MIXED WOOD PLAINS AND MIXED WOOD SHIELD", "HIGHLANDS AND APPALACHIAN FORESTS"), "NA_L2NAME"] <- "CENTRAL AND MIXED WOODS AND HIGHLANDS FORESTS"
#      #//
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 1"), "NA_L2NAME"] <- "WESTERN CORDILLERA AND UPPER GILA MOUNTAINS 1"
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("CENTRAL AND MIXED WOOD PLAINS AND MIXED WOOD SHIELD", "HIGHLANDS AND APPALACHIAN FORESTS"), "NA_L2NAME"] <- "CENTRAL AND MIXED WOODS AND HIGHLANDS FORESTS"
# 
#   }
# 
# } else if (ecoregion == "forest" & response == "CAMCover") {
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("OZARK/OUACHITA-APPALACHIAN FORESTS", "SOUTHEASTERN USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN PLAINS AND APPALACHIAN FORESTS"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "MARINE WEST COAST AND WESTERN CORDILLERA"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS", "SOUTHEASTERN PLAINS AND APPALACHIAN FORESTS"), "NA_L2NAME"] <- "SOUTHEASTERN PLAINS AND APPALACHIAN FORESTS"
# 
#   #///
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("OZARK/OUACHITA-APPALACHIAN FORESTS", "SOUTHEASTERN USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN PLAINS AND APPALACHIAN FORESTS"
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MARINE WEST COAST FOREST", "WESTERN CORDILLERA"), "NA_L2NAME"] <- "MARINE WEST COAST AND WESTERN CORDILLERA"
# 
#   modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS", "SOUTHEASTERN PLAINS AND APPALACHIAN FORESTS"), "NA_L2NAME"] <- "SOUTHEASTERN PLAINS AND APPALACHIAN FORESTS"
# 
# } else if (ecoregion == "eastForest") {
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("EVERGLADES", "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"), "NA_L2NAME"] <- "EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS","CENTRAL USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN AND CENTRAL USA PLAINS"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD SHIELD", "ATLANTIC HIGHLANDS"), "NA_L2NAME"] <- "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS", "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD"), "NA_L2NAME"] <- "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD AND PLAINS"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("SOUTHEASTERN AND CENTRAL USA PLAINS", "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD AND PLAINS"), "NA_L2NAME"] <- "PLAINS AND HIGHLANDS AND SHIELD"
# 
#   modDat_1_s[modDat_1_s$NA_L2NAME %in% c("EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "SOUTHEASTERN USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN PLAINS AND COAST"
# 
#   # #////
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("EVERGLADES", "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"), "NA_L2NAME"] <- "EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS","CENTRAL USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN AND CENTRAL USA PLAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD SHIELD", "ATLANTIC HIGHLANDS"), "NA_L2NAME"] <- "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS", "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD"), "NA_L2NAME"] <- "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD AND PLAINS"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("SOUTHEASTERN AND CENTRAL USA PLAINS", "ATLANTIC HIGHLANDS AND MIXED WOOD SHIELD AND PLAINS"), "NA_L2NAME"] <- "PLAINS AND HIGHLANDS AND SHIELD"
# 
#    modDat_1_sf[modDat_1_sf$NA_L2NAME %in% c("EVERGLADES MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS", "SOUTHEASTERN USA PLAINS"), "NA_L2NAME"] <- "SOUTHEASTERN PLAINS AND COAST"
# 
#    ## divide southeastern US plains into two regions, since it's by far the largest group
#   # modDat_1_s[modDat_1_s$NA_L2NAME == "SOUTHEASTERN USA PLAINS" &
#   #              modDat_1_s$Lat < -590062, "NA_L2NAME"] <- "SOUTHEASTERN USA PLAINS 1"
#   # modDat_1_s[modDat_1_s$NA_L2NAME == "SOUTHEASTERN USA PLAINS", #&
#   #             # modDat_1_s$Lat < -590062,
#   #            "NA_L2NAME"] <- "SOUTHEASTERN USA PLAINS 2"
# 
#   #   ## divide southeastern US plains into two regions, since it's by far the largest group
#   # modDat_1_s[modDat_1_s$NA_L2NAME == "OZARK/OUACHITA-APPALACHIAN FORESTS" &
#   #              modDat_1_s$Long < 854862.2, "NA_L2NAME"] <- "OZARK/OUACHITA-APPALACHIAN FORESTS 1"
#   # modDat_1_s[modDat_1_s$NA_L2NAME == "OZARK/OUACHITA-APPALACHIAN FORESTS" &
#   #              modDat_1_s$Long  >=   854862.2, "NA_L2NAME"] <- "OZARK/OUACHITA-APPALACHIAN FORESTS 2"
# }
# make a table of n for each region

modDat_1_s %>% 
  group_by(NA_L2NAME) %>% 
  dplyr::summarize("Number_Of_Observations" = length(NA_L2NAME)) %>% 
  rename("Level_2_Ecoregion" = NA_L2NAME)%>% 
  kable() %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

Level_2_Ecoregion	Number_Of_Observations
ATLANTIC HIGHLANDS	998
CENTRAL USA PLAINS	77
COLD DESERTS	174835
EVERGLADES	4
MARINE WEST COAST FOREST	4689
MEDITERRANEAN CALIFORNIA	17370
MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS	1516
MIXED WOOD PLAINS	1062
MIXED WOOD SHIELD	1172
OZARK/OUACHITA-APPALACHIAN FORESTS	1963
SOUTH CENTRAL SEMIARID PRAIRIES	108217
SOUTHEASTERN USA PLAINS	2265
TAMAULIPAS-TEXAS SEMIARID PLAIN	7242
TEMPERATE PRAIRIES	14425
TEXAS-LOUISIANA COASTAL PLAIN	4422
UPPER GILA MOUNTAINS	5510
WARM DESERTS	66037
WEST-CENTRAL SEMIARID PRAIRIES	85020
WESTERN CORDILLERA	43174
WESTERN SIERRA MADRE PIEDMONT	7278

Then, look at the spatial distribution and environmental characteristics of the grouped ecoregions

map1 <- ggplot() +
  geom_sf(data=cropped_states,fill='white') +
  geom_sf(data=modDat_1_sf#[modDat_1_sf$NA_L2NAME %in% c("MIXED WOOD PLAINS"),]
          ,
          aes(fill=as.factor(NA_L2NAME)),linewidth=0.5,alpha=0.5) +
  geom_point(data=modDat_1_s#[modDat_1_s$NA_L2NAME %in% c("MIXED WOOD PLAINS"),]
             ,
             alpha=0.5, 
             aes(x = x, y = y, color=as.factor(NA_L2NAME)), alpha = .1) +
  #scale_fill_okabeito() +
  #scale_color_okabeito() +
 # theme_default() +
  theme(legend.position = 'none') +
  labs(title = "Level 2 Ecoregions as spatial blocks")

hull <- modDat_1_sf %>%
  ungroup() %>%
  group_by(NA_L2NAME) %>%
  slice(chull(tmean, prcp))

plot1<-ggplot(data=modDat_1_sf,aes(x=tmean,y=prcp)) +
  geom_polygon(data = hull, alpha = 0.25,aes(fill=NA_L2NAME) )+
  geom_point(aes(group=NA_L2NAME,color=NA_L2NAME),alpha=0.25) +
  theme_minimal() + xlab("Annual Average T_mean - long-term average") +
  ylab("Annual Average Precip - long-term average") #+
  #scale_color_okabeito() +
  #scale_fill_okabeito()

plot2<-ggplot(data=modDat_1_sf %>%
                pivot_longer(cols=tmean:prcp),
              aes(x=value,group=name)) +
  # geom_polygon(data = hull, alpha = 0.25,aes(fill=fold) )+
  geom_density(aes(group=NA_L2NAME,fill=NA_L2NAME),alpha=0.25) +
  theme_minimal() +
  facet_wrap(~name,scales='free')# +
  #scale_color_okabeito() +
  #scale_fill_okabeito()
 
library(patchwork)
(combo <- (map1+plot1)/plot2) 

# 
# ggplot(data = modDat_1_s) +
#   geom_density(aes(ShrubCover_transformed, col = NA_L2NAME)) +
#   xlim(c(0,100))

Fit a global model with all of the data

First, fit a LASSO regression model using the glmnet R package

• This regression is a beta glm with a logit link (using custom function from Daniel)
• Use cross validation across level 2 ecoregions to tune the lambda parameter in the LASSO model
• this model is fit to using the scaled weather/climate/soils variables
• this list of possible predictors includes:
  1. main effects
  2. interactions between all soils variables
  3. interactions between climate and weather variables
  4. transformed main effects (squared, log-transformed (add a uniform integer – 20– to all variables prior to log-transformation), square root-transformed (add a uniform integer – 20– to all variables prior to log-transformation))

Get rid of transformed predictions and interactions that are correlated

# get first pass of names correlated variables
X_df <- X %>% 
  as.data.frame() %>% 
  dplyr::select(-'(Intercept)')  
corrNames_i <- X_df %>% 
  cor()  %>% 
   caret::findCorrelation(cutoff = .7, verbose = FALSE, names = TRUE, exact = TRUE)
# remove those names that are untransformed main effects 
  # vector of columns to remove 
badNames <- corrNames_i[!(corrNames_i %in% prednames)]
while (sum(!(corrNames_i %in% prednames))>0) {
 corrNames_i <-  X_df %>% 
    dplyr::select(-badNames) %>% 
     cor()  %>% 
   caret::findCorrelation(cutoff = .7, verbose = FALSE, names = TRUE, exact = TRUE)
 # update the vector of names to remove 
 badNames <- unique(c(badNames, corrNames_i[!(corrNames_i %in% prednames)]))
}

## see if there are any correlated variables left (would be all main effects at this point)
# if there are, step through and remove the variable that each is most correlated with 
if (length(corrNames_i)>1) {
  for (i in 1:length(corrNames_i)) {
    X_i <- X_df %>% 
      dplyr::select(-badNames)
    if (corrNames_i[i] %in% names(X_i)) {
    corMat_i <- cor(x = X_i[corrNames_i[i]], y = X_i %>% dplyr::select(-corrNames_i[i])) 
    badNames_i <- colnames(corMat_i)[abs(corMat_i)>=.7]
    # if there are any predictors in the 'badNames_i', remove them from this list
    if (length(badNames_i) > 0 & sum(c(badNames_i %in% prednames))>0) {
        badNames_i <- badNames_i[!(badNames_i %in% prednames)]
    }
    badNames <- unique(c(badNames, badNames_i))
    }
  }
}
## update the X matrix to exclude these correlated variables
X <- X[,!(colnames(X) %in% badNames)]

if (run == TRUE) {
  # set up custom folds
    # get the ecoregions for training lambda
  train_eco <- modDat_1_s$NA_L2NAME#[train]
  
  # Fit model -----------------------------------------------
  # specify leave-one-year-out cross-validation
  my_folds <- as.numeric(as.factor(train_eco))

    # set up parallel processing
    library(doMC)
    # this computer has 16 cores (parallel::detectCores())
    registerDoMC(cores = 8)
    
    fit <- cv.glmnet(
      x = X[,2:ncol(X)], 
      y = y, 
      family = "binomial",
      keep = FALSE,
      alpha = 1,  # 0 == ridge regression, 1 == lasso, 0.5 ~~ elastic net
      lambda = lambdas,
      relax = ifelse(response == "ShrubCover", yes = TRUE, no = FALSE),
      #nlambda = 100,
      type.measure="mse",
      #penalty.factor = pen_facts,
      foldid = my_folds,
      #thresh = thresh,
      standardize = FALSE, ## scales variables prior to the model sequence... coefficients are always returned on the original scale
      parallel = TRUE
    )
    base::saveRDS(fit, paste0("../ModelFitting/models/yesOrNoTrees_globalLASSOmod_binomial.rds"))
    
  
     best_lambda <- fit$lambda.min
  # save the lambda for the most regularized model w/ an MSE that is still 1SE w/in the best lambda model
  lambda_1SE <- fit$lambda.1se
  # save the lambda for the most regularized model w/ an MSE that is still .5SE w/in the best lambda model
  lambda_halfSE <- best_lambda + ((lambda_1SE - best_lambda)/2)
 
## Now, we need to do stability selection to ensure the coefficients that are being chosen with each lambda are stable 

## stability selection for best lambda model 
# setup params
p <- ncol(X[,2:ncol(X)]) # of parameters
n <- length(y) # of observations
n_iter <- 100        # number of subsamples
sample_frac <- 0.75  # fraction of data to subsample
lambda_val <- best_lambda    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_bestL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = "binomial",
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  select_bestL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_bestL[select_bestL] <- selection_counts_bestL[select_bestL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected over 100 iterations)
selection_prob_bestL <- selection_counts_bestL / n_iter
selection_prob_bestL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_bestL)
)

# get those variables that are selected in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
bestLambda_coef <- selection_prob_bestL_df[selection_prob_bestL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

#//////
# stability selection for 1se lambda model
lambda_val <-  lambda_1SE    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_1seL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = "binomial",
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  selected_1seL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_1seL[selected_1seL] <- selection_counts_1seL[selected_1seL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected over 100 iterations)
selection_prob_1seL <- selection_counts_1seL / n_iter
selection_prob_1seL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_1seL)
)

# get those variables that are selected in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
seLambda_coef <- selection_prob_1seL_df[selection_prob_1seL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

# stability selection for half se lambda model
lambda_val <- lambda_halfSE    # fixed lambda value (could be chosen via CV)

# Track selection
selection_counts_halfseL <- matrix(0, nrow = p, ncol = 1)

for (i in 1:n_iter) {
  # Subsample rows
  sample_idx <- sample(1:n, size = floor(sample_frac * n), replace = FALSE)
  X_sub <- X[sample_idx, ]
  y_sub <- y[sample_idx]

  # Fit Lasso model
  fit_stab_i <- glmnet(x = X_sub[,2:ncol(X_sub)], y = y_sub, 
    family = "binomial",
    alpha = 1, lambda = lambda_val, standardize = FALSE)

  # Get non-zero coefficients (excluding intercept)
  selected_halfseL <- which(as.vector(coef(fit_stab_i))[-1] != 0)
  selection_counts_halfseL[selected_halfseL] <- selection_counts_halfseL[selected_halfseL] + 1
}

# Convert counts to selection probabilities (the probability that a variable is selected_halfseL over 100 iterations)
selection_prob_halfseL <- selection_counts_halfseL / n_iter
selection_prob_halfseL_df <- data.frame(
  VariableNumber = paste0("X", 1:p),
  VariableName = rownames(coef(fit_stab_i))[2:(p+1)],
  SelectionProb = as.vector(selection_prob_halfseL)
)

# get those variables that are selected_halfseL_halfseL in ≥70% of subsets (Meinshausen and Bühlmann, 2010)
halfseLambda_coef <- selection_prob_halfseL_df[selection_prob_halfseL_df$SelectionProb>=.7, c("VariableName", "SelectionProb")]

## fit w/ the identified coefficients from the 'best' lambda, but using the glm function
  mat_glmnet_best <- bestLambda_coef$VariableName 

  if (length(mat_glmnet_best) == 0) {
    f_glm_bestLambda <- as.formula(paste0("TotalTreeCover_binom", "~ 1"))
  } else {
  f_glm_bestLambda <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(mat_glmnet_best, collapse = " + ")))
  }
  
## fit using betareg
  fit_glm_bestLambda <- fit_glm_bestLambda_binomial <- glm(formula = f_glm_bestLambda, data = modDat_1_s, family = binomial)
    
   ## fit w/ the identified coefficients from the '1se' lambda, but using the glm function
  mat_glmnet_1se <- seLambda_coef$VariableName
    
  if (length(mat_glmnet_1se) == 0) {
    f_glm_1se <- as.formula(paste0("TotalTreeCover_binom", "~ 1"))
  } else {
  f_glm_1se <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(mat_glmnet_1se, collapse = " + ")))
  }


  fit_glm_se <- glm(formula = f_glm_1se, data = modDat_1_s, family = binomial)
  # glm(data = modDat_1_s, formula = f_glm_1se,
  #                   family =  stats::Gamma(link = "log"))
  
     ## fit w/ the identified coefficients from the '.5se' lambda, but using the glm function
  mat_glmnet_halfse <- halfseLambda_coef$VariableName
  
  if (length(mat_glmnet_halfse) == 0) {
    f_glm_halfse <- as.formula(paste0("TotalTreeCover_binom", "~ 1"))
  } else {
  f_glm_halfse <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(mat_glmnet_halfse, collapse = " + ")))
  }

  fit_glm_halfse <- glm(formula = f_glm_halfse, data = modDat_1_s, family = binomial )
  
  ## save models 
  saveRDS(fit_glm_bestLambda, paste0("./models/yesOrNoTrees_bestLambdaGLM.rds"))
  saveRDS(fit_glm_halfse, paste0("./models/yesOrNoTrees_halfSELambdaGLM.rds"))
  saveRDS(fit_glm_se, paste0("./models/yesOrNoTrees_oneSELambdaGLM.rds"))
    
  ## save the R environment after running the models 
  save(f_glm_halfse, mat_glmnet_halfse, halfseLambda_coef,
              f_glm_1se, mat_glmnet_1se, seLambda_coef,
              f_glm_bestLambda, mat_glmnet_best, bestLambda_coef,
              file = paste0("./models/interimModelFittingObjects_yesOrNoTrees_binomial.rds" ))
  } else {
    # read in LASSO object
    fit <- readRDS("../ModelFitting/models/yesOrNoTrees_globalLASSOmod_binomial.rds")
    
    # read in R objects having to do w/ model fitting 
    load(file = paste0("./models/interimModelFittingObjects_yesOrNoTrees_binomial.rds"))
      
  fit_glm_bestLambda <- readRDS("./models/yesOrNoTrees_bestLambdaGLM.rds")
  fit_glm_halfse <- readRDS("./models/yesOrNoTrees_halfSELambdaGLM.rds")
  fit_glm_se <- readRDS("./models/yesOrNoTrees_oneSELambdaGLM.rds")
  }


  # assess model fit
  # assess.glmnet(fit$fit.preval, #newx = X[,2:293], 
  #               newy = y, family = stats::Gamma(link = "log"))
  # save the minimum lambda
  best_lambda <- fit$lambda.min
  # save the lambda for the most regularized model w/ an MSE that is still 1SE w/in the best lambda model
  lambda_1SE <- fit$lambda.1se
  # save the lambda for the most regularized model w/ an MSE that is still .5SE w/in the best lambda model
  lambda_halfSE <- best_lambda + ((lambda_1SE - best_lambda)/2)
 
  print(fit)     

## 
## Call:  cv.glmnet(x = X[, 2:ncol(X)], y = y, lambda = lambdas, type.measure = "mse",      foldid = my_folds, keep = FALSE, parallel = TRUE, relax = ifelse(response ==          "ShrubCover", yes = TRUE, no = FALSE), family = "binomial",      alpha = 1, standardize = FALSE) 
## 
## Measure: Mean-Squared Error 
## 
##       Lambda Index Measure      SE Nonzero
## min 0.002583   120  0.2601 0.03829      23
## 1se 0.015703    94  0.2981 0.03679      13

  plot(fit)

Then, we predict (on the training set) using both of these models (best lambda and 1se lambda)

  ## predict on the test data
  # lasso model predictions with the optimal lambda
  optimal_pred <- predict(fit_glm_bestLambda, newx=X[,2:ncol(X)], type = "response")
  optimal_pred_1se <-  predict(fit_glm_se, newx=X[,2:ncol(X)], type = "response")
  optimal_pred_halfse <- predict(fit_glm_halfse, newx = X[,2:ncol(X)], type = "response")
  
    null_fit <- glm(
      formula = y ~ 1, #data = modDat_1_s, 
      family = binomial
      )
  null_pred <- predict(null_fit, newdata = as.data.frame(X), type = "response"
                       )

  # save data
  fullModOut <- list(
    "modelObject" = fit,
    "nullModelObject" = null_fit,
    "modelPredictions" = data.frame(#ecoRegion_holdout = rep(test_eco,length(y)),
      obs=y,
                    pred_opt=optimal_pred, 
                    pred_opt_se = optimal_pred_1se,
                    pred_opt_halfse = optimal_pred_halfse,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ))

ggplot() + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$obs), col = "black", alpha = .1) + 
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt), col = "red", alpha = .1) + ## predictions w/ the CV model
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_halfse), col = "orange", alpha = .1) + ## predictions w/ the CV model (.5se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_opt_se), col = "green", alpha = .1) + ## predictions w/ the CV model (1se lambda)
  geom_point(aes(X[,2], fullModOut$modelPredictions$pred_null), col = "blue", alpha = .1) + 
  labs(title = "A rough comparison of observed and model-predicted values", 
       subtitle = "black = observed values \n red = predictions from 'best lambda' model \n orange = predictions for '1/2se' lambda model \n green = predictions from '1se' lambda model \n blue = predictions from null model") +
  xlab(colnames(X)[2])

  #ylim(c(0,200))

The internal cross-validation process to fit the global LASSO model identified an optimal lambda value (regularization parameter) of r{print(best_lambda)}. The lambda value such that the cross validation error is within 1 standard error of the minimum (“1se lambda”) was `r{print(fit$lambda.1se)}`` . The following coefficients were kept in each model:

# the coefficient matrix from the 'best model' -- find and print those coefficients that aren't 0 in a table
coef_glm_bestLambda <- coef(fit_glm_bestLambda) %>% 
  data.frame() 
coef_glm_bestLambda$coefficientName <- rownames(coef_glm_bestLambda)
names(coef_glm_bestLambda)[1] <- "coefficientValue_bestLambda"
# coefficient matrix from the '1se' model 
coef_glm_1se <- coef(fit_glm_se) %>% 
  data.frame() 
coef_glm_1se$coefficientName <- rownames(coef_glm_1se)
names(coef_glm_1se)[1] <- "coefficientValue_1seLambda"
# coefficient matrix from the 'half se' model 
coef_glm_halfse <- coef(fit_glm_halfse) %>% 
  data.frame() 
coef_glm_halfse$coefficientName <- rownames(coef_glm_halfse)
names(coef_glm_halfse)[1] <- "coefficientValue_halfseLambda"
# add together
coefs <- full_join(coef_glm_bestLambda, coef_glm_halfse) %>% 
  full_join(coef_glm_1se) %>% 
  dplyr::select(coefficientName, coefficientValue_bestLambda,
                coefficientValue_halfseLambda, coefficientValue_1seLambda)

globModTerms <- coefs[!is.na(coefs$coefficientValue_bestLambda), "coefficientName"]

## also, get the number of unique variables in each model 
var_prop_pred <- paste0(response, "_pred")
response_vars <- c(response, var_prop_pred)
# for best lambda model
prednames_fig <- paste(str_split(globModTerms, ":", simplify = TRUE)) 
prednames_fig <- str_replace(prednames_fig, "I\\(", "")
prednames_fig <- str_replace(prednames_fig, "\\^2\\)", "")
prednames_fig <- unique(prednames_fig[prednames_fig>0])
prednames_fig <- prednames_fig
prednames_fig_num <- length(prednames_fig)
# for 1SE lambda model
globModTerms_1se <- coefs[!is.na(coefs$coefficientValue_1seLambda), "coefficientName"]
if (length(globModTerms_1se) == 1) {
prednames_fig_1se <- paste(str_split(globModTerms_1se, ":", simplify = TRUE)) 
prednames_fig_1se <- str_replace(prednames_fig_1se, "I\\(", "")
prednames_fig_1se <- str_replace(prednames_fig_1se, "\\^2\\)", "")
prednames_fig_1se <- unique(prednames_fig_1se[prednames_fig_1se>0])
prednames_fig_1se_num <- c(0)
} else {
prednames_fig_1se <- paste(str_split(globModTerms_1se, ":", simplify = TRUE)) 
prednames_fig_1se <- str_replace(prednames_fig_1se, "I\\(", "")
prednames_fig_1se <- str_replace(prednames_fig_1se, "\\^2\\)", "")
prednames_fig_1se <- unique(prednames_fig_1se[prednames_fig_1se>0])
prednames_fig_1se_num <- length(prednames_fig_1se)
}
# for 1/2SE lambda model
globModTerms_halfse <- coefs[!is.na(coefs$coefficientValue_halfseLambda), "coefficientName"]
if (length(globModTerms_halfse) == 1) {
prednames_fig_halfse <- paste(str_split(globModTerms_halfse, ":", simplify = TRUE)) 
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "I\\(", "")
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "\\^2\\)", "")
prednames_fig_halfse <- unique(prednames_fig_halfse[prednames_fig_halfse>0])
prednames_fig_halfse_num <- c(0)
} else {
prednames_fig_halfse <- paste(str_split(globModTerms_halfse, ":", simplify = TRUE)) 
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "I\\(", "")
prednames_fig_halfse <- str_replace(prednames_fig_halfse, "\\^2\\)", "")
prednames_fig_halfse <- unique(prednames_fig_halfse[prednames_fig_halfse>0])
prednames_fig_halfse_num <- length(prednames_fig_halfse)
}
# make a table
kable(coefs, col.names = c("Coefficient Name", "Value from best lambda model", 
                           "Value from 1/2 se lambda", "Value from 1se lambda model")
      ) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

Coefficient Name	Value from best lambda model	Value from 1/2 se lambda	Value from 1se lambda model
(Intercept)	-0.2751679	-0.7333348	-1.4935932
prcp	2.7438954	2.2338082	0.6676509
prcp_seasonality	-0.4090616	-0.6781704	-1.1027383
prcpTempCorr	-0.4762006	-0.5993745	-0.5735991
isothermality	0.0819259	NA	NA
annWetDegDays	0.2477627	0.1446735	0.9726790
coarse	0.5044160	0.1776674	0.2746722
AWHC	-0.6056629	-0.6161314	-0.8089169
I(tmean^2)	-0.1018303	NA	NA
I(prcp_seasonality^2)	0.0778928	0.0400178	0.0428878
I(prcpTempCorr^2)	-0.4893370	-0.6935534	NA
I(isothermality^2)	0.1249780	0.2432939	0.1154969
I(sand^2)	-0.3031629	-0.2622575	-0.4135753
I(AWHC^2)	0.1727775	0.1399819	NA
prcp:annWetDegDays	-0.6922608	-1.0646284	NA
prcpTempCorr:annWetDegDays	-0.6514052	NA	NA
prcp:isothermality	-0.1348763	NA	NA
isothermality:tmean	-0.2639748	NA	NA
prcp:prcpTempCorr	1.0668523	0.5575201	0.3356435
prcp:tmean	0.4926712	1.1040206	NA
prcp_seasonality:prcpTempCorr	-0.2426936	-0.4608979	-0.5169076
coarse:AWHC	0.3042161	NA	NA
AWHC:sand	-0.1872696	NA	NA
coarse:sand	-0.2844443	-0.1923460	NA
tmean:isothermality	NA	-0.2904138	NA
prcp:prcp_seasonality	NA	-0.5641012	NA
annWetDegDays:tmean	NA	NA	-0.1142478
prcp_seasonality:isothermality	NA	NA	-0.0630637

# calculate RMSE of all models 
RMSE_best <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt")], truth = "obs", estimate = "pred_opt")$.estimate
RMSE_halfse <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt_halfse")], truth = "obs", estimate = "pred_opt_halfse")$.estimate
RMSE_1se <- yardstick::rmse(fullModOut$modelPredictions[,c("obs", "pred_opt_se")], truth = "obs", estimate = "pred_opt_se")$.estimate
# calculate bias of all models
bias_best <-  mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt)
bias_halfse <-  mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt_halfse)
bias_1se <- mean((fullModOut$modelPredictions$obs) - fullModOut$modelPredictions$pred_opt_se)

uniqueCoeffs <- data.frame("Best lambda model" = c(signif(RMSE_best,3), as.character(signif(bias_best, 3)),
  as.integer(length(globModTerms)-1), as.integer(prednames_fig_num), 
                                                   as.integer(sum(prednames_fig %in% c(prednames_clim))),
                                                   as.integer(sum(prednames_fig %in% c(prednames_weath))),
                                                   as.integer(sum(prednames_fig %in% c(prednames_soils)))
                                                   ), 
                           "1/2 se lambda model" = c(signif(RMSE_halfse,3), as.character(signif(bias_halfse, 3)),
                             length(globModTerms_halfse)-1, prednames_fig_halfse_num,
                                                   sum(prednames_fig_halfse %in% c(prednames_clim)),
                                                   sum(prednames_fig_halfse %in% c(prednames_weath)),
                                                   sum(prednames_fig_halfse %in% c(prednames_soils))), 
                           "1se lambda model" = c(signif(RMSE_1se,3), as.character(signif(bias_1se, 3)),
                             length(globModTerms_1se)-1, prednames_fig_1se_num,
                                                   sum(prednames_fig_1se %in% c(prednames_clim)),
                                                   sum(prednames_fig_1se %in% c(prednames_weath)),
                                                   sum(prednames_fig_1se %in% c(prednames_soils))))
row.names(uniqueCoeffs) <- c("RMSE", "bias: mean(obs-pred.)", "Total number of coefficients", "Number of unique coefficients",
                             "Number of unique climate coefficients", 
                             "Number of unique weather coefficients",  
                             "Number of unique soils coefficients"
                             )

kable(uniqueCoeffs, 
      col.names = c("Best lambda model", "1/2 se lambda model", "1se lambda model"), row.names = TRUE) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed")) 

	Best lambda model	1/2 se lambda model	1se lambda model
RMSE	0.329	0.332	0.339
bias: mean(obs-pred.)	-1.58e-10	-5.59e-11	-2.98e-13
Total number of coefficients	23	18	13
Number of unique coefficients	9	9	9
Number of unique climate coefficients	6	6	6
Number of unique weather coefficients	0	0	0
Number of unique soils coefficients	3	3	3

Visualizations of Model Predictions and Residuals – using best lambda model

observed vs. predicted values

As the alternative to the best lambda model, use the model (1se or 1/2se of best Lambda) that has the fewest number of unique predictors

if (whichSecondBestMod == "auto") {
  # name of model w/ fewest # of predictors (but more than 0)
uniqueCoeff_min <- min(as.numeric(uniqueCoeffs[4,2:3])[which(as.numeric(uniqueCoeffs[4,2:3]) > 0)])
alternativeModel <- names(uniqueCoeffs[4,2:3])[which(uniqueCoeffs[4,2:3] == uniqueCoeff_min)]

if (is.finite(uniqueCoeff_min)) {
  if (length(alternativeModel) == 1) {
  if (alternativeModel == "X1.2.se.lambda.model") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
} else if (alternativeModel == "X1se.lambda.model") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
}
} else {
  # if both alternative models have the same number of unique coefficients, chose the model that has the fewest number of total predictors
  uniqueCoeff_min2 <- min(as.numeric(uniqueCoeffs[3,alternativeModel]))
alternativeModel2 <- names(uniqueCoeffs[3,alternativeModel])[which(uniqueCoeffs[3,alternativeModel] == uniqueCoeff_min2)]
if (alternativeModel2 == "X1.2.se.lambda.model") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
} else if (alternativeModel2 == "X1se.lambda.model") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
}
}
  }else {
    mod_secondBest <- NULL
  name_secondBestMod <- "Intercept_Only"
  prednames_secondBestMod <- NULL
}
} else if (whichSecondBestMod == "1se") {
  mod_secondBest <- fit_glm_se
  name_secondBestMod <- "1 SE Model"
  prednames_secondBestMod <- prednames_fig_1se
} else if (whichSecondBestMod == "halfse") {
  mod_secondBest <- fit_glm_halfse
  name_secondBestMod <- "1/2 SE Model"
  prednames_secondBestMod <- prednames_fig_halfse
}

Predicting on the data

  # create prediction for each each model
# (i.e. for each fire proporation variable)
predict_by_response <- function(mod, df) {
  df_out <- df
  response_name <- paste0("TotalTreeCover_binom", "_pred")
  preds <- predict(mod, newx= df_out, #s="lambda.min", 
                                     type = "response")
  preds[preds<0] <- 0
  #preds[preds>100] <- 100
  df_out <- df_out %>% cbind(preds)
   colnames(df_out)[ncol(df_out)] <- response_name
  return(df_out)
}

pred_glm1 <- predict_by_response(fit_glm_bestLambda, X[,2:ncol(X)])

## back-transform the 
# add back in true y values
pred_glm1 <- pred_glm1 %>% 
  cbind(data.frame("TotalTreeCover_binom" = modDat_1_s$TotalTreeCover_binom))

# add back in lat/long data 
pred_glm1 <- pred_glm1 %>% 
  cbind(modDat_1_s[,c("x", "y", "Year")])

pred_glm1$resid <- pred_glm1[,"TotalTreeCover_binom"] - pred_glm1[,paste0("TotalTreeCover_binom", "_pred")]
pred_glm1$extremeResid <- NA
pred_glm1[pred_glm1$resid > .5 | pred_glm1$resid < -.5,"extremeResid"] <- 1

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

pred_glm1_1se <- predict_by_response(mod_secondBest, X[,2:ncol(X)])

# add back in true y values
pred_glm1_1se <- pred_glm1_1se %>% 
  cbind(data.frame("TotalTreeCover_binom" = modDat_1_s$TotalTreeCover_binom))

# add back in lat/x data 
pred_glm1_1se <- pred_glm1_1se %>% 
  cbind(modDat_1_s[,c("x", "y", "Year")])

pred_glm1_1se$resid <- pred_glm1_1se[,"TotalTreeCover_binom"] - pred_glm1_1se[,paste0("TotalTreeCover_binom", "_pred")]
pred_glm1_1se$extremeResid <- NA
pred_glm1_1se[pred_glm1_1se$resid > .5 | pred_glm1_1se$resid < -.5,"extremeResid"] <- 1
}

Maps of Observations, Predictions, and Residuals=

Observations across the temporal range of the dataset

# rasterize
# get reference raster
test_rast <-  rast("../../../Data_raw/dayMet/rawMonthlyData/orders/70e0da02b9d2d6e8faa8c97d211f3546/Daymet_Monthly_V4R1/data/daymet_v4_prcp_monttl_na_1980.tif") %>%
  terra::aggregate(fact = 3, fun = "mean") %>% 
  terra::project(crs("EPSG:4326"))

## |---------|---------|---------|---------|=========================================                                          |---------|---------|---------|---------|=========================================                                          

  # transform to match format of veg. data 
  
## add ecoregion boundaries (for our ecoregion level model)
regions <- sf::st_read(dsn = "../../../Data_raw/Level2Ecoregions/", layer = "NA_CEC_Eco_Level2") 

## Reading layer `NA_CEC_Eco_Level2' from data source 
##   `/Users/astears/Documents/Dropbox_static/Work/NAU_USGS_postdoc/cleanPED/PED_vegClimModels/Data_raw/Level2Ecoregions' 
##   using driver `ESRI Shapefile'
## Simple feature collection with 2261 features and 8 fields
## Geometry type: POLYGON
## Dimension:     XY
## Bounding box:  xmin: -4334052 ymin: -3313739 xmax: 3324076 ymax: 4267265
## Projected CRS: Sphere_ARC_INFO_Lambert_Azimuthal_Equal_Area

regions <- regions %>% 
  st_transform(crs = st_crs(test_rast)) %>% 
  st_make_valid() 

ecoregionLU <- data.frame("NA_L1NAME" = sort(unique(regions$NA_L1NAME)), 
                        "newRegion" = c(NA, "Forest", "dryShrubGrass", 
                                        "dryShrubGrass", "Forest", "dryShrubGrass",
                                       "dryShrubGrass", "Forest", "Forest", 
                                       "dryShrubGrass", "Forest", "Forest", 
                                       "Forest", "Forest", "dryShrubGrass", 
                                       NA
                                        ))
goodRegions <- regions %>% 
  left_join(ecoregionLU)
mapRegions <- goodRegions %>% 
  filter(!is.na(newRegion)) %>% 
  group_by(newRegion) %>% 
  summarise(geometry = sf::st_union(geometry)) %>% 
  ungroup() %>% 
  st_simplify(dTolerance = 1000) %>% 
  st_crop(ext(-130, -60, 20, 60))

# rasterize data
plotObs <- pred_glm1 %>% 
         drop_na("TotalTreeCover_binom") %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = "TotalTreeCover_binom", 
                   fun = function(x) {
                     round(mean(x))
                   }) %>% 
  terra::crop(ext(-130, -60, 20, 60))

# make shapefile of cropped state boundaries in appropriate crs
cropped_states_2 <- cropped_states %>% 
  st_transform(crs = "EPSG:4326") %>% 
  st_make_valid() %>% 
  st_crop(ext(-130, -60, 20, 60))

# make figures
map_obs <- ggplot() +
geom_spatraster(data = plotObs) + 
  geom_sf(data=cropped_states_2 ,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Observations of Binomial Total Tree Cover")) +
  scale_fill_gradient2(low = "brown",
                       mid = "wheat" ,
                       high = "darkgreen" , 
                       midpoint = 0,   na.value = "darkgrey") + 
  xlim(-125, -65) + 
  ylim(25, 50)

hist_obs <- ggplot(pred_glm1) + 
  geom_histogram(aes(TotalTreeCover_binom), fill = "lightgrey", col = "darkgrey")

library(ggpubr)
ggarrange(map_obs, hist_obs, heights = c(3,1), ncol = 1)

Predictions across the temporal range of the dataset

# rasterize data
plotPred <- pred_glm1 %>% 
         drop_na(paste0("TotalTreeCover_binom","_pred")) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = paste0("TotalTreeCover_binom","_pred"), 
                   fun = mean) %>% 
  terra::crop(ext(-130, -60, 20, 60))

# make figures
map_preds1 <- ggplot() +
geom_spatraster(data = plotPred) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the 'best lambda' fitted model of Yes/No Trees"),
     subtitle =  "bestLambda model")  +
  scale_fill_gradient2(low = "wheat",
                       mid = "darkgreen",
                       high = "red" , 
                       midpoint = 1,   na.value = "darkgrey",
                       limits = c(0,1)) + 
  xlim(-125, -65) + 
  ylim(25, 50)

hist_preds1 <- ggplot(pred_glm1) + 
  geom_histogram(aes(.data[[paste0("TotalTreeCover_binom", "_pred")]]), fill = "lightgrey", col = "darkgrey")+ 
  xlim(c(0,1))

ggarrange(map_preds1, hist_preds1, heights = c(3,1), ncol = 1)

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

# rasterize data
plotPred <- pred_glm1_1se %>% 
         drop_na(paste0("TotalTreeCover_binom","_pred")) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = paste0("TotalTreeCover_binom","_pred"), 
                   fun = mean) %>% 
     terra::crop(ext(-130, -60, 20, 60))

# make figures
map_preds2 <- ggplot() +
geom_spatraster(data = plotPred) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Predictions from the ", name_secondBestMod, " of Yes/No Trees"),
     subtitle =  name_secondBestMod)  +
  scale_fill_gradient2(low = "wheat",
                       mid = "darkgreen",
                       high = "red" , 
                       midpoint = 1,   na.value = "darkgrey",
                       limits = c(0, 1))  + 
  xlim(-125, -65) + 
  ylim(25, 50)

hist_preds2 <- ggplot(pred_glm1_1se) + 
  geom_histogram(aes(.data[[paste0("TotalTreeCover_binom", "_pred")]]), fill = "lightgrey", col = "darkgrey")+ 
  xlim(c(0,1))

ggarrange(map_preds2, hist_preds2, heights = c(3,1), ncol = 1)
}

# rasterize data
plotResid_rast <- pred_glm1 %>% 
         drop_na(resid) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = "resid", 
                   fun = mean) %>% 
     terra::crop(ext(-130, -60, 20, 60))

# identify locations where residuals are >.5 or < -.5
badResids_high <- pred_glm1 %>% 
  filter(resid > .5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) 
badResids_low <- pred_glm1 %>% 
  filter(resid < -.5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) 
# make figures
map <- ggplot() +
geom_spatraster(data =plotResid_rast) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  #geom_sf(data = badResids_high, col = "blue") +
  #geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Resids. (obs. - pred.) from the model of Yes/No Trees"),
     subtitle = "bestLambda model \n red points indicate locations that have residuals below -.5 \n blue points indicate locations that have residuals above .5") +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" , 
                       midpoint = 0,   na.value = "darkgrey",
                       limits = c(-1,1)
                       ) + 
  xlim(-125, -65) + 
  ylim(25, 50)

hist <- ggplot(pred_glm1) + 
  geom_histogram(aes(resid), fill = "lightgrey", col = "darkgrey") + 
  # geom_text(aes(x = min(resid)*.9, y = 1500, label = paste0("min = ", round(min(resid),2)))) +
  # geom_text(aes(x = max(resid)*.9, y = 1500, label = paste0("max = ", round(max(resid),2)))) + 
  geom_vline(aes(xintercept = mean(resid)))

ggarrange(map, hist, heights = c(3,1), ncol = 1)

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {

# rasterize data
plotResid_rast <- pred_glm1_1se %>% 
         drop_na(resid) %>% 
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) %>% 
  terra::rasterize(y = test_rast, 
                   field = "resid", 
                   fun = mean) %>% 
     terra::crop(ext(-130, -60, 20, 60))

# identify locations where residuals are >10 or < -10
badResids_high <- pred_glm1_1se %>% 
  filter(resid > .5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) 
badResids_low <- pred_glm1_1se %>% 
  filter(resid < -.5)  %>% 
  terra::vect(geom = c("x", "y")) %>% 
  terra::set.crs(crs(test_rast)) 
# make figures
map <- ggplot() +
geom_spatraster(data =plotResid_rast) + 
  geom_sf(data=cropped_states_2,fill=NA )  + 
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
  # geom_sf(data = badResids_high, col = "blue") +
  # geom_sf(data = badResids_low, col = "red") +
labs(title = paste0("Resids. (obs. - pred.) from the model of Yes/No Trees"),
     subtitle = paste0(name_secondBestMod,"\n red points indicate locations that have residuals below -.5 \n blue points indicate locations that have residuals above .5")) +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" , 
                       midpoint = 0,   na.value = "darkgrey",
                       limits = c(-1,1)
                       )  + 
  xlim(-125, -65) + 
  ylim(25, 50)
hist <- ggplot(pred_glm1_1se) + 
  geom_histogram(aes(resid), fill = "lightgrey", col = "darkgrey") + 
 # geom_text(aes(x = min(resid)*.9, y = 1500, label = paste0("min = ", round(min(resid),2)))) +
  #geom_text(aes(x = max(resid)*.9, y = 1500, label = paste0("max = ", round(max(resid),2))))+ 
  geom_vline(aes(xintercept = mean(resid)))

ggarrange(map, hist, heights = c(3,1), ncol = 1)
}

Are there biases of the model predictions across year/lat/long?

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  # plot residuals against Year
yearResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = jitter(Year), y = resid), alpha = .1) + 
  geom_smooth(aes(x = Year, y = resid)) + 
  xlab("Year") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")

# plot residuals against Lat
latResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = y, y = resid), alpha = .1) + 
  geom_smooth(aes(x = y, y = resid)) + 
  xlab("Latitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")

# plot residuals against Long
longResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = x, y = resid), alpha = .1) + 
  geom_smooth(aes(x = x, y = resid)) + 
  xlab("Longitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
library(patchwork)
(yearResidMod_bestLambda ) / 
(  latResidMod_bestLambda ) /
(  longResidMod_bestLambda )
} else {

# plot residuals against Year
yearResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = jitter(Year), y = resid), alpha = .1) + 
  geom_smooth(aes(x = Year, y = resid)) + 
  xlab("Year") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
yearResidMod_1seLambda <- ggplot(pred_glm1_1se) + 
  geom_point(aes(x = jitter(Year), y = resid), alpha = .1) + 
  geom_smooth(aes(x = Year, y = resid)) + 
  xlab("Year") + 
  ylab("Residuals") +
  ggtitle(paste0("from ", name_secondBestMod))

# plot residuals against Lat
latResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = y, y = resid), alpha = .1) + 
  geom_smooth(aes(x = y, y = resid)) + 
  xlab("Latitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
latResidMod_1seLambda <- ggplot(pred_glm1_1se) + 
  geom_point(aes(x = y, y = resid), alpha = .1) + 
  geom_smooth(aes(x = y, y = resid)) + 
  xlab("Latitude") + 
  ylab("Residuals") +
  ggtitle(paste0("from ", name_secondBestMod))

# plot residuals against Long
longResidMod_bestLambda <- ggplot(pred_glm1) + 
  geom_point(aes(x = x, y = resid), alpha = .1) + 
  geom_smooth(aes(x = x, y = resid)) + 
  xlab("Longitude") + 
  ylab("Residuals") +
  ggtitle("from best lamba model")
longResidMod_1seLambda <- ggplot(pred_glm1_1se) + 
  geom_point(aes(x = x, y = resid), alpha = .1) + 
  geom_smooth(aes(x = x, y = resid)) + 
  xlab("Longitude") + 
  ylab("Residuals") +
  ggtitle(paste0("from ", name_secondBestMod))

library(patchwork)
(yearResidMod_bestLambda + yearResidMod_1seLambda) / 
(  latResidMod_bestLambda + latResidMod_1seLambda) /
(  longResidMod_bestLambda + longResidMod_1seLambda)
}

Quantile plots

Binning predictor variables into “Quantiles” and looking at the mean predicted probability for each percentile.

response_vars <- c("TotalTreeCover_binom", "TotalTreeCover_binom_pred")
# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles <- predvars2deciles(pred_glm1,
                                      response_vars = response_vars,
                                        pred_vars = prednames_fig, 
                                       cut_points = seq(0, 1, 0.01))
}
# get deciles for 1 SE lambda model 
if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")} else {
  pred_glm1_deciles_1se <- predvars2deciles(pred_glm1_1se,
                                      response_vars = response_vars,
                                        pred_vars = prednames_secondBestMod, 
                                       cut_points = seq(0, 1, 0.01))
  }

Below are quantile plots for the best lambda model (note that the predictor variables are scaled)

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {

# publication quality version
g3 <- decile_dotplot_pq(df = pred_glm1_deciles, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), IQR = FALSE,
                        CI = FALSE
                        ) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), dfRaw = pred_glm1, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("../../../Figures/CoverDatFigures/ figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Below are percentile plots from the second best lambda model ()

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
  } else {

# publication quality version
g3 <- decile_dotplot_pq(pred_glm1_deciles_1se, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), IQR = FALSE) + ggtitle("Decile Plot")

g4 <- add_dotplot_inset(g3, df = pred_glm1_deciles_1se, response = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")), dfRaw = pred_glm1_1se, add_smooth = TRUE, deciles = FALSE)

  
if(save_figs) {
  # png(paste0("figures/quantile_plots/quantile_plot_", response,  "_",ecoregion,".png"), 
  #    units = "in", res = 600, width = 5.5, height = 3.5 )
  #   print(g4)
  # dev.off()
}

g4
}

Filtered Quantiles

For the best lambda model

Filtered ‘Quantile’ plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower 20th percentiles of each predictor variable.

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_fig,
                         filter_var = TRUE,
                         filter_vars = prednames_fig,
                         cut_points = seq(0, 1, 0.01)) 
g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Filtered quantile figure with middle 2 deciles also shown

if ( name_secondBestMod == "Intercept_Only") {
  print("The next best lambda model only contains one predictor (an intercept)")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_fig,
                         filter_vars = prednames_fig,
                         filter_var = TRUE,
                         add_mid = TRUE,
                         cut_points = seq(0, 1, 0.01))

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6)
#   g 
# dev.off()
}
g
}

For the second best lambda model ()

Filtered ‘Quantile’ plots of data. These plots show each vegetation variable, but only based on data that falls into the upper and lower 20th percentiles of each predictor variable.

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  
pred_glm1_deciles_filt <- predvars2deciles( pred_glm1_1se, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_secondBestMod,
                         filter_var = TRUE,
                         filter_vars = prednames_secondBestMod,
                         cut_points = seq(0, 1, 0.01)) 
g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)

if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Filtered quantile figure with middle 2 deciles also shown

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
pred_glm1_deciles_filt_mid <- predvars2deciles(pred_glm1, 
                         response_vars = c("TotalTreeCover_binom", paste0("TotalTreeCover_binom", "_pred")),
                         pred_vars = prednames_secondBestMod,
                         filter_vars = prednames_secondBestMod,
                         filter_var = TRUE,
                         add_mid = TRUE,
                         cut_points = seq(0, 1, 0.01))

g <- decile_dotplot_filtered_pq(df = pred_glm1_deciles_filt_mid, response = "TotalTreeCover_binom", 
                                xvars = prednames_fig)


if(save_figs) {
# jpeg(paste0("figures/quantile_plots/quantile_plot_filtered_mid_v1", , ".jpeg"),
#      units = "in", res = 600, width = 5.5, height = 6 )
#   g 
# dev.off()
}
g
}

Show model RMSE w/in each quantile

# get deciles for best lambda model 
if (length(prednames_fig) == 0) {
  print("The best lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles %>% 
    ggplot(aes(x = mean_value, y = RMSE)) +
    facet_wrap(~name, scales = "free_x") +
    geom_point(alpha = .2, size = .5) + 
    geom_smooth(lwd = .5) + 
    xlab("Scaled predictor value") + 
    ggtitle("RMSE by decile for bestLambda model")
}

# get deciles for 1 SE lambda model 
if (length(prednames_secondBestMod) == 0) {
  print("The 1SE (or 1/2 SE) lambda model only contains one predictor (an intercept), so decile plots aren't possible to generate")
} else {
  pred_glm1_deciles_1se %>% 
    ggplot(aes(x = mean_value, y = RMSE)) +
    facet_wrap(~name, scales = "free_x") +
    geom_point(alpha = .2, size = .5) + 
    geom_smooth(lwd = .5) + 
    xlab("Scaled predictor value") + 
    ggtitle(paste0("RMSE by decile for ", name_secondBestMod, "model"))
}

Cross-validation

Using best lambda model

Use terms from global model to re-fit and predict on different held out regions

Figures show residuals for each of the models fit to held-out ecoregions

These models were fit to six ecoregions, and then predict on the indicated heldout ecoregion

if (length(prednames_fig) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {

## code from Tredennick et al. 2020
# try each separate level II ecoregion as a test set
# make a list to hold output data
outList <- vector(mode = "list", length = length(sort(unique(modDat_1_s$NA_L2NAME))))
# obs_pred <- data.frame(ecoregion = character(),obs = numeric(),
#                        pred_opt = numeric(), pred_null = numeric()#,
#                        #pred_nopenalty = numeric()
#                        )

## get the model specification from the global model
mat <- as.matrix(coef(fit_glm_bestLambda, s = "lambda.min"))
mat2 <- mat[mat[,1] != 0,]

f_cv <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(names(mat2)[2:length(names(mat2))], collapse = " + ")))

X_cv <- model.matrix(object = f_cv, data = modDat_1_s)
# get response variable
y_cv <- as.matrix(modDat_1_s[,"TotalTreeCover_binom"])


# now, loop through so with each iteration, a different ecoregion is held out
 for(i_eco in sort(unique(modDat_1_s$NA_L2NAME))){

  # split into training and test sets
  test_eco <- i_eco
  print(test_eco)
  # identify the rowID of observations to be in the training and test datasets
  train <- which(modDat_1_s$NA_L2NAME!=test_eco) # data for all ecoregions that aren't 'i_eco'
  test <- which(modDat_1_s$NA_L2NAME==test_eco) # data for the ecoregion that is 'i_eco'

  trainDat_all <- modDat_1_s %>%
    slice(train) %>%
    dplyr::select(-newRegion)
  testDat_all <- modDat_1_s %>%
    slice(test) %>%
    dplyr::select(-newRegion)

  # get the model matrices for input and response variables for cross validation model specification
  X_train <- as.matrix(X_cv[train,])
  X_test <- as.matrix(X_cv[test,])

  y_train <- modDat_1_s[train,"TotalTreeCover_binom"]
  y_test <- modDat_1_s[test,"TotalTreeCover_binom"]

  # get the model matrices for input and response variables for original model specification
  X_train_glob <- as.matrix(X[train,])
  X_test_glob <- as.matrix(X[test,])

  y_train_glob <- modDat_1_s[train,"TotalTreeCover_binom"]
  y_test_glob <- modDat_1_s[test,"TotalTreeCover_binom"]

  train_eco <- modDat_1_s$NA_L2NAME[train]

  ## just try a regular glm w/ the components from the global model
  fit_i <- glm(data = trainDat_all, formula = f_cv,
    ,
               family =  binomial
    )
    
  # lasso model predictions with the optimal lambda (back transformed)
  optimal_pred <- predict(fit_i, newdata = testDat_all, type = "response") 
  # null model and predictions
  # the "null" model in this case is the global model
  # predict on the test data for this iteration w/ the global model (back transformed)
  null_pred <- predict.glm(fit_glm_bestLambda, newdata = testDat_all, type = "response") 

  # save data
  tmp <- data.frame(ecoRegion_holdout = rep(test_eco,length(y_test)),
                    obs=y_test,
                    pred_opt=optimal_pred,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ) %>%
    cbind(testDat_all)

  # calculate RMSE, bias, etc. of
  # RMSE of CV model
  RMSE_optimal <- yardstick::rmse(data = data.frame(optimal_pred,"y_test" = (y_test)), truth = "y_test", estimate = "optimal_pred")[1,]$.estimate
  # RMSE of global model
  RMSE_null <- yardstick::rmse(data = data.frame(null_pred,"y_test" = (y_test)), truth = "y_test", estimate = "null_pred")[1,]$.estimate
  # bias of CV model
  bias_optimal <- mean((y_test) - optimal_pred)
  # bias of global model
  bias_null <-  mean((y_test) - null_pred )

  # put output into a list
  tmpList <- list("testRegion" = i_eco,
    "modelObject" = fit_i,
       "modelPredictions" = tmp,
    "performanceMetrics" = data.frame("RMSE_cvModel" = RMSE_optimal,
                                      "RMSE_globalModel" = RMSE_null,
                                      "bias_cvModel" = bias_optimal,
                                      "bias_globalModel" = bias_null))

  # save model outputs
  outList[[which(sort(unique(modDat_1_s$NA_L2NAME)) == i_eco)]] <- tmpList
 }
}

## [1] "ATLANTIC HIGHLANDS"
## [1] "CENTRAL USA PLAINS"
## [1] "COLD DESERTS"
## [1] "EVERGLADES"
## [1] "MARINE WEST COAST FOREST"
## [1] "MEDITERRANEAN CALIFORNIA"
## [1] "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"
## [1] "MIXED WOOD PLAINS"
## [1] "MIXED WOOD SHIELD"
## [1] "OZARK/OUACHITA-APPALACHIAN FORESTS"
## [1] "SOUTH CENTRAL SEMIARID PRAIRIES"
## [1] "SOUTHEASTERN USA PLAINS"
## [1] "TAMAULIPAS-TEXAS SEMIARID PLAIN"
## [1] "TEMPERATE PRAIRIES"
## [1] "TEXAS-LOUISIANA COASTAL PLAIN"
## [1] "UPPER GILA MOUNTAINS"
## [1] "WARM DESERTS"
## [1] "WEST-CENTRAL SEMIARID PRAIRIES"
## [1] "WESTERN CORDILLERA"
## [1] "WESTERN SIERRA MADRE PIEDMONT"

Below are the RMSE and bias values for predictions made for each holdout level II ecoregion, compared to predictions from the global model for that same ecoregion

# table of model performance
purrr::map(outList, .f = function(x) {
  cbind(data.frame("holdout region" = x$testRegion),  x$performanceMetrics)
}
) %>%
  purrr::list_rbind() %>%
  kable(col.names = c("Held-out ecoregion", "RMSE of CV model", "RMSE of global model",
                      "bias of CV model - mean(obs-pred.)", "bias of global model- mean(obs-pred.)"),
        caption = "Performance of Cross Validation using 'best lambda' model specification") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))

Performance of Cross Validation using ‘best lambda’ model specification

Held-out ecoregion	RMSE of CV model	RMSE of global model	bias of CV model - mean(obs-pred.)	bias of global model- mean(obs-pred.)
ATLANTIC HIGHLANDS	0.0945964	0.0945940	-0.0063873	-0.0063638
CENTRAL USA PLAINS	0.2481843	0.2481098	0.0479814	0.0478416
COLD DESERTS	0.3774933	0.3558885	0.0469372	0.0098149
EVERGLADES	0.4993849	0.4964655	0.4538083	0.4505955
MARINE WEST COAST FOREST	0.6083767	0.5539055	0.2952746	0.1436718
MEDITERRANEAN CALIFORNIA	0.4381348	0.4136707	-0.0772256	-0.0063344
MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS	0.5883081	0.5197511	-0.2915907	-0.1950038
MIXED WOOD PLAINS	0.2515497	0.2491878	0.0680605	0.0661145
MIXED WOOD SHIELD	0.6095819	0.5535376	0.5137187	0.4451055
OZARK/OUACHITA-APPALACHIAN FORESTS	0.1482538	0.1482652	-0.0096196	-0.0093031
SOUTH CENTRAL SEMIARID PRAIRIES	0.3188133	0.2862631	-0.0355981	-0.0097361
SOUTHEASTERN USA PLAINS	0.1978258	0.1917639	0.0807824	0.0700857
TAMAULIPAS-TEXAS SEMIARID PLAIN	0.4423868	0.4353828	0.1138859	0.0793969
TEMPERATE PRAIRIES	0.5497150	0.3973539	0.3487009	0.1654049
TEXAS-LOUISIANA COASTAL PLAIN	0.5019485	0.4754651	-0.0885628	-0.0353010
UPPER GILA MOUNTAINS	0.5339175	0.5308870	0.0054276	0.0098206
WARM DESERTS	0.1664917	0.1603402	-0.0318083	-0.0187646
WEST-CENTRAL SEMIARID PRAIRIES	0.2083615	0.1835227	-0.0895522	-0.0428393
WESTERN CORDILLERA	0.5381310	0.5114102	0.0052660	0.0253901
WESTERN SIERRA MADRE PIEDMONT	0.3743765	0.3599220	-0.1322874	-0.1010854

# visualize model predictions
for (i in 1:length(unique(modDat_1_s$NA_L2NAME))) {
  holdoutRegion <- outList[[i]]$testRegion
  predictionData <- outList[[i]]$modelPredictions
  modTerms <- as.matrix(coef(outList[[i]]$modelObject)) %>%
    as.data.frame() %>%
    filter(V1!=0) %>%
    rownames()

  # calculate residuals
  predictionData <- predictionData %>%
  mutate(resid = .[["obs"]] - .[["pred_opt"]] ,
         resid_globMod = .[["obs"]]  - .[["pred_null"]])

# rasterize
# use 'test_rast' from earlier
  # rasterize data
plotObs <- predictionData %>%
         drop_na(paste("TotalTreeCover_binom")) %>%
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs(test_rast)) %>%
  terra::rasterize(y = test_rast,
                   field = "resid",
                   fun = mean)

tempExt <- crds(plotObs, na.rm = TRUE)

plotObs_2 <- plotObs %>%
  terra::crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2]))
       )

# make figures
# make histogram
hist_i <- ggplot(predictionData) +
  geom_histogram(aes(resid_globMod), col = "darkgrey", fill = "lightgrey") +
  xlab(c("Residuals (obs. - pred.)"))
# make map
map_i <-  ggplot() +
geom_spatraster(data = plotObs_2) +
  geom_sf(data=cropped_states_2,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Residuals (obs. - pred.) for predictions of \n", holdoutRegion, " \n from a model fit to other ecoregions"),
     subtitle = paste0("TotalTreeCover_binom", " ~ ", paste0( modTerms, collapse = " + "))) +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" ,
                       midpoint = 0,   na.value = "darkgrey",
                       limits = c(-1, 1))   + 
  xlim(st_bbox(plotObs_2)[1],st_bbox(plotObs_2)[3]) + 
  ylim(st_bbox(plotObs_2)[2],st_bbox(plotObs_2)[4])

 assign(paste0("residPlot_",holdoutRegion),
   value = ggarrange(map_i, hist_i, heights = c(3,1), ncol = 1)
)

}

  lapply(unique(modDat_1_s$NA_L2NAME), FUN = function(x) {
    get(paste0("residPlot_", x))
  })

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Using second best lambda model (either 1se or 1/2se)

Use terms from global model to re-fit and predict on different held out regions

Figures show residuals for each of the models fit to held-out ecoregions

These models were fit to six ecoregions, and then predict on the indicated heldout ecoregion

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {

## code from Tredennick et al. 2020
# try each separate level II ecoregion as a test set
# make a list to hold output data
outList <- vector(mode = "list", length = length(sort(unique(modDat_1_s$NA_L2NAME))))

## get the model specification from the global model
mat <- as.matrix(coef(mod_secondBest, s = "lambda.min"))
mat2 <- mat[mat[,1] != 0,]

f_cv <- as.formula(paste0("TotalTreeCover_binom", " ~ ", paste0(names(mat2)[2:length(names(mat2))], collapse = " + ")))

X_cv <- model.matrix(object = f_cv, data = modDat_1_s)
# get response variable
y_cv <- as.matrix(modDat_1_s[,"TotalTreeCover_binom"])


# now, loop through so with each iteration, a different ecoregion is held out
 for(i_eco in sort(unique(modDat_1_s$NA_L2NAME))){

  # split into training and test sets
  test_eco <- i_eco
  print(test_eco)
  # identify the rowID of observations to be in the training and test datasets
  train <- which(modDat_1_s$NA_L2NAME!=test_eco) # data for all ecoregions that aren't 'i_eco'
  test <- which(modDat_1_s$NA_L2NAME==test_eco) # data for the ecoregion that is 'i_eco'

  trainDat_all <- modDat_1_s %>%
    slice(train) %>%
    dplyr::select(-newRegion)
  testDat_all <- modDat_1_s %>%
    slice(test) %>%
    dplyr::select(-newRegion)

  # get the model matrices for input and response variables for cross validation model specification
  X_train <- as.matrix(X_cv[train,])
  X_test <- as.matrix(X_cv[test,])

  y_train <- modDat_1_s[train,"TotalTreeCover_binom"]
  y_test <- modDat_1_s[test,"TotalTreeCover_binom"]

  # get the model matrices for input and response variables for original model specification
  X_train_glob <- as.matrix(X[train,])
  X_test_glob <- as.matrix(X[test,])

  y_train_glob <- modDat_1_s[train,"TotalTreeCover_binom"]
  y_test_glob <- modDat_1_s[test,"TotalTreeCover_binom"]

  train_eco <- modDat_1_s$NA_L2NAME[train]

  ## just try a regular glm w/ the components from the global model
  fit_i <- glm(data = trainDat_all, formula = f_cv,
    ,
               family =  binomial
    )

    coef(fit_i)

  # lasso model predictions with the optimal lambda
  optimal_pred <- predict(fit_i, newdata= testDat_all, type = "response") 
  # null model and predictions
  # the "null" model in this case is the global model
  # predict on the test data for this iteration w/ the global model
  null_pred <- predict.glm(mod_secondBest, newdata = testDat_all, type = "response") 

  # save data
  tmp <- data.frame(ecoRegion_holdout = rep(test_eco,length(y_test)),
                    obs=y_test,
                    pred_opt=optimal_pred,
                    pred_null=null_pred#,
                    #pred_nopenalty=nopen_pred
                    ) %>%
    cbind(testDat_all)

  # calculate RMSE, bias, etc. of
  # RMSE of CV model
  RMSE_optimal <- yardstick::rmse(data = data.frame(optimal_pred, "y_test" = (y_test)), truth = "y_test", estimate = "optimal_pred")[1,]$.estimate
  # RMSE of global model
  RMSE_null <- yardstick::rmse(data = data.frame(null_pred,  "y_test" = (y_test)), truth = "y_test", estimate = "null_pred")[1,]$.estimate
  # bias of CV model
  bias_optimal <- mean((y_test) - optimal_pred)
  # bias of global model
  bias_null <-  mean((y_test) - null_pred )

  # put output into a list
  tmpList <- list("testRegion" = i_eco,
    "modelObject" = fit_i,
       "modelPredictions" = tmp,
    "performanceMetrics" = data.frame("RMSE_cvModel" = RMSE_optimal,
                                      "RMSE_globalModel" = RMSE_null,
                                      "bias_cvModel" = bias_optimal,
                                      "bias_globalModel" = bias_null))

  # save model outputs
  outList[[which(sort(unique(modDat_1_s$NA_L2NAME)) == i_eco)]] <- tmpList
 }
}

## [1] "ATLANTIC HIGHLANDS"
## [1] "CENTRAL USA PLAINS"
## [1] "COLD DESERTS"
## [1] "EVERGLADES"
## [1] "MARINE WEST COAST FOREST"
## [1] "MEDITERRANEAN CALIFORNIA"
## [1] "MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS"
## [1] "MIXED WOOD PLAINS"
## [1] "MIXED WOOD SHIELD"
## [1] "OZARK/OUACHITA-APPALACHIAN FORESTS"
## [1] "SOUTH CENTRAL SEMIARID PRAIRIES"
## [1] "SOUTHEASTERN USA PLAINS"
## [1] "TAMAULIPAS-TEXAS SEMIARID PLAIN"
## [1] "TEMPERATE PRAIRIES"
## [1] "TEXAS-LOUISIANA COASTAL PLAIN"
## [1] "UPPER GILA MOUNTAINS"
## [1] "WARM DESERTS"
## [1] "WEST-CENTRAL SEMIARID PRAIRIES"
## [1] "WESTERN CORDILLERA"
## [1] "WESTERN SIERRA MADRE PIEDMONT"

Below are the RMSE and bias values for predictions made for each holdout level II ecoregion, compared to predictions from the global model for that same ecoregion

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {
# table of model performance
purrr::map(outList, .f = function(x) {
  cbind(data.frame("holdout region" = x$testRegion),  x$performanceMetrics)
}
) %>%
  purrr::list_rbind() %>%
  kable(col.names = c("Held-out ecoregion", "RMSE of CV model", "RMSE of global model",
                      "bias of CV model - mean(obs-pred.)", "bias of global model - mean(obs-pred.)"),
        caption = "Performance of Cross Validation using 'second best lambda' model specification") %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed"))
}

Performance of Cross Validation using ‘second best lambda’ model specification

Held-out ecoregion	RMSE of CV model	RMSE of global model	bias of CV model - mean(obs-pred.)	bias of global model - mean(obs-pred.)
ATLANTIC HIGHLANDS	0.0946700	0.0946699	-0.0022295	-0.0022201
CENTRAL USA PLAINS	0.2522781	0.2522195	0.0540135	0.0538909
COLD DESERTS	0.3828966	0.3728097	-0.0145829	0.0090631
EVERGLADES	0.0756120	0.0755781	0.0473302	0.0473074
MARINE WEST COAST FOREST	0.5397591	0.5376235	-0.0232534	-0.0112243
MEDITERRANEAN CALIFORNIA	0.4664631	0.4520852	-0.0223799	0.0138058
MISSISSIPPI ALLUVIAL AND SOUTHEAST USA COASTAL PLAINS	0.6864780	0.6602017	-0.4621305	-0.4305467
MIXED WOOD PLAINS	0.2178009	0.2169264	0.0486855	0.0476229
MIXED WOOD SHIELD	0.4129083	0.3947138	0.3221233	0.3009906
OZARK/OUACHITA-APPALACHIAN FORESTS	0.1482848	0.1482775	-0.0075204	-0.0073364
SOUTH CENTRAL SEMIARID PRAIRIES	0.3120015	0.2897741	-0.0070999	-0.0084849
SOUTHEASTERN USA PLAINS	0.1932074	0.1921759	0.0445593	0.0428788
TAMAULIPAS-TEXAS SEMIARID PLAIN	0.4429024	0.4394973	0.1047246	0.0896147
TEMPERATE PRAIRIES	0.5316319	0.4150013	0.3125085	0.1521276
TEXAS-LOUISIANA COASTAL PLAIN	0.5449456	0.5460867	-0.0918364	-0.0558813
UPPER GILA MOUNTAINS	0.5632281	0.5578316	0.2157609	0.2003996
WARM DESERTS	0.2197187	0.1662993	-0.1031044	-0.0307030
WEST-CENTRAL SEMIARID PRAIRIES	0.1958684	0.1803319	-0.0847095	-0.0554471
WESTERN CORDILLERA	0.5161143	0.5085663	0.0620542	0.0585882
WESTERN SIERRA MADRE PIEDMONT	0.3514059	0.3503739	-0.0257453	-0.0243693

if (length(prednames_secondBestMod) == 0) {
  print("The model only contains one predictor (an intercept), so cross validation isn't practical")
} else {
for (i in 1:length(unique(modDat_1_s$NA_L2NAME))) {
  holdoutRegion <- outList[[i]]$testRegion
  predictionData <- outList[[i]]$modelPredictions
  modTerms <- as.matrix(coef(outList[[i]]$modelObject)) %>%
    as.data.frame() %>%
    filter(V1!=0) %>%
    rownames()

  # calculate residuals
  predictionData <- predictionData %>%
  mutate(resid = .[["obs"]] - .[["pred_opt"]] ,
         resid_globMod = .[["obs"]]  - .[["pred_null"]])


# rasterize
# use 'test_rast' from earlier

  # rasterize data
plotObs <- predictionData %>%
         drop_na(paste("TotalTreeCover_binom")) %>%
  #slice_sample(n = 5e4) %>%
  terra::vect(geom = c("x", "y")) %>%
  terra::set.crs(crs(test_rast)) %>%
  terra::rasterize(y = test_rast,
                   field = "resid",
                   fun = mean) 

tempExt <- crds(plotObs, na.rm = TRUE)

plotObs_2 <- plotObs %>%
  crop(ext(min(tempExt[,1]), max(tempExt[,1]),
           min(tempExt[,2]), max(tempExt[,2]))
       )

# make figures
# make histogram
hist_i <- ggplot(predictionData) +
  geom_histogram(aes(resid_globMod), col = "darkgrey", fill = "lightgrey") +
  xlab(c("Residuals (obs. - pred.)"))
# make map
map_i <-  ggplot() +
geom_spatraster(data = plotObs_2) +
  geom_sf(data=cropped_states_2,fill=NA ) +
  geom_sf(data = mapRegions, fill = NA, col = "orchid", lwd = .5) +
labs(title = paste0("Residuals (obs. - pred.) for predictions of \n", holdoutRegion, " \n from a model fit to other ecoregions"),
     subtitle = paste0("TotalTreeCover_binom", " ~ ", paste0( modTerms, collapse = " + "))) +
  scale_fill_gradient2(low = "red",
                       mid = "white" ,
                       high = "blue" ,
                       midpoint = 0,   na.value = "darkgrey",
                       limits = c(-1, 1))  + 
  xlim(st_bbox(plotObs_2)[1],st_bbox(plotObs_2)[3]) + 
  ylim(st_bbox(plotObs_2)[2],st_bbox(plotObs_2)[4])

 assign(paste0("residPlot_",holdoutRegion),
   value = ggarrange(map_i, hist_i, heights = c(3,1), ncol = 1)
)

}

  lapply(unique(modDat_1_s$NA_L2NAME), FUN = function(x) {
    get(paste0("residPlot_", x))
  })
}

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Save output

## save the coefficients for the models (best lambda, 1/2se lambda, 1se lambda)
if(trimAnom == TRUE) {
saveRDS(coefs, file = paste0("./models/yesOrNoTrees_modelCoefficients.rds"))
saveRDS(uniqueCoeffs, file = paste0("./models/yesOrNoTrees_modelMetrics_trimAnom.rds"))
} else {
saveRDS(coefs, file = paste0("./models/yesOrNoTrees_modelCoefficients.rds"))
saveRDS(uniqueCoeffs, file = paste0("./models/yesOrNoTrees_modelMetrics_trimAnom.rds"))
}
# make a table

## partial dependence plots
#vip::vip(mod_glmFinal, num_features = 15)

#pdp_all_vars(mod_glmFinal, mod_vars = pred_vars, ylab = 'probability',train = df_small)

#caret::varImp(fit)

session info

Hash of current commit (i.e. to ID the version of the code used)

system("git rev-parse HEAD", intern=TRUE)

## [1] "af89c366ebe4eb850e89a4bee3846f63e8f3461c"

Packages etc.

sessionInfo()

## R version 4.5.2 (2025-10-31)
## Platform: aarch64-apple-darwin20
## Running under: macOS Sequoia 15.6.1
## 
## Matrix products: default
## BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.1
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## time zone: America/Denver
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] ggpubr_0.6.2               factoextra_1.0.7          
##  [3] USA.state.boundaries_1.0.1 glmnet_4.1-10             
##  [5] Matrix_1.7-4               kableExtra_1.4.0          
##  [7] rsample_1.3.1              here_1.0.2                
##  [9] StepBeta_2.1.0             ggtext_0.1.2              
## [11] knitr_1.50                 gridExtra_2.3             
## [13] pdp_0.8.2                  GGally_2.4.0              
## [15] lubridate_1.9.4            forcats_1.0.1             
## [17] stringr_1.6.0              dplyr_1.1.4               
## [19] purrr_1.2.0                readr_2.1.6               
## [21] tidyr_1.3.1                tibble_3.3.0              
## [23] tidyverse_2.0.0            caret_7.0-1               
## [25] lattice_0.22-7             ggplot2_4.0.1             
## [27] sf_1.0-22                  tidyterra_0.7.2           
## [29] terra_1.8-80               ggspatial_1.1.10          
## [31] betareg_3.2-4              dtplyr_1.3.2              
## [33] patchwork_1.3.2           
## 
## loaded via a namespace (and not attached):
##   [1] RColorBrewer_1.1-3   wk_0.9.4             rstudioapi_0.17.1   
##   [4] jsonlite_2.0.0       shape_1.4.6.1        magrittr_2.0.4      
##   [7] modeltools_0.2-24    farver_2.1.2         rmarkdown_2.30      
##  [10] vctrs_0.6.5          rstatix_0.7.3        htmltools_0.5.8.1   
##  [13] broom_1.0.10         s2_1.1.9             Formula_1.2-5       
##  [16] pROC_1.19.0.1        sass_0.4.10          parallelly_1.46.0   
##  [19] KernSmooth_2.23-26   bslib_0.9.0          plyr_1.8.9          
##  [22] sandwich_3.1-1       zoo_1.8-15           cachem_1.1.0        
##  [25] commonmark_2.0.0     lifecycle_1.0.4      iterators_1.0.14    
##  [28] pkgconfig_2.0.3      R6_2.6.1             fastmap_1.2.0       
##  [31] future_1.68.0        digest_0.6.38        furrr_0.3.1         
##  [34] rprojroot_2.1.1      textshaping_1.0.4    labeling_0.4.3      
##  [37] yardstick_1.3.2      timechange_0.3.0     mgcv_1.9-3          
##  [40] abind_1.4-8          compiler_4.5.2       proxy_0.4-27        
##  [43] aod_1.3.3            withr_3.0.2          S7_0.2.1            
##  [46] backports_1.5.0      carData_3.0-5        DBI_1.2.3           
##  [49] ggstats_0.12.0       ggsignif_0.6.4       MASS_7.3-65         
##  [52] lava_1.8.2           classInt_0.4-11      gtools_3.9.5        
##  [55] ModelMetrics_1.2.2.2 tools_4.5.2          units_1.0-0         
##  [58] lmtest_0.9-40        future.apply_1.20.1  nnet_7.3-20         
##  [61] glue_1.8.0           nlme_3.1-168         gridtext_0.1.5      
##  [64] grid_4.5.2           reshape2_1.4.5       generics_0.1.4      
##  [67] recipes_1.3.1        gtable_0.3.6         tzdb_0.5.0          
##  [70] class_7.3-23         data.table_1.17.8    hms_1.1.4           
##  [73] xml2_1.5.0           car_3.1-3            flexmix_2.3-20      
##  [76] markdown_2.0         ggrepel_0.9.6        foreach_1.5.2       
##  [79] pillar_1.11.1        splines_4.5.2        survival_3.8-3      
##  [82] tidyselect_1.2.1     litedown_0.8         svglite_2.2.2       
##  [85] stats4_4.5.2         xfun_0.54            hardhat_1.4.2       
##  [88] timeDate_4051.111    stringi_1.8.7        yaml_2.3.10         
##  [91] evaluate_1.0.5       codetools_0.2-20     cli_3.6.5           
##  [94] rpart_4.1.24         systemfonts_1.3.1    jquerylib_0.1.4     
##  [97] Rcpp_1.1.0           globals_0.18.0       parallel_4.5.2      
## [100] gower_1.0.2          listenv_0.10.0       viridisLite_0.4.2   
## [103] ipred_0.9-15         scales_1.4.0         prodlim_2025.04.28  
## [106] e1071_1.7-16         combinat_0.0-8       rlang_1.1.6         
## [109] cowplot_1.2.0